It is known that the initial‐boundary value problem for certain integrable Partial Differential
Equations (PDEs) on the half‐line with integrable boundary conditions can be mapped to a …

We present a framework to solve the open problem of formulating the inverse scattering
method (ISM) for an integrable PDE on a star-graph. The idea is to map the problem on the …

This study focuses on the impurities in integrable models from the viewpoint of generalized
hydrodynamics (GHD). An impurity can be thought of as a boundary condition for the GHD …

We establish the algebraic origin of the following observations made previously by the
authors and coworkers:(i) A given integrable PDE in 1+ 1 dimensions within the Zakharov …

We define and illustrate the novel notion of dual integrable hierarchies, on the example of
the nonlinear Schrödinger (NLS) hierarchy. For each integrable nonlinear evolution …

In recent years, new properties of space-time duality in the Hamiltonian formalism of certain
integrable classical field theories have been discovered and have led to their reformulation …

A bstract We introduce the concept of multisymplectic formalism, familiar in covariant field
theory, for the study of integrable defects in 1+ 1 classical field theory. The main idea is the …

A bstract The construction of type II Bäcklund transformation for the sine-Gordon and the
Tzitzéica-Bullough-Dodd models are obtained from gauge transformation. An infinite …

A bstract A systematic approach to Liouville integrable defects is proposed, based on an
underlying Poisson algebraic structure. The non-linear Schrödinger model in the presence …

Affine Toda field theories with a purely transmitting integrable defect are considered and the
model based on a 2 is analysed in detail. After providing a complete characterization of the …